3. Production runs of gasoline are tested for their octane level. Because of slight variations in environmental conditions and oil characteristics, the octane levels vary slightly. Suppose that, based upon past experience, the engineers know that the octane level is distributed normally, with a mean of 87 and a standard deviation of 0.25.
a. What is the probability that the next production run will have an octane level greater than 87?
b. What is the probability that the next production run will have an octane level greater than 87.7?
c. What is the probability that the next production run will have an octane level between 86.5 and 87.5?
d. Complete the following sentence (rounding your answer to two decimal places): “Ninety-five percent of production runs will have an octane level above ___.”
e. Complete the following sentence (rounding your answer to two decimal places): “Ninety percent of production runs will have an octane level below ___.”
f. Complete the following sentence (rounding your answer to two decimal places): “Ninety-nine percent of production runs will have an octane level between ___ and ___.”